Details

sample41.0ms

Algorithm

intervals

Results

15.0ms	401×	body	80	valid
5.0ms	157×	body	80	nan

simplify102.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	24	7
1	53	5
2	106	5
3	269	5
4	904	5
5	3976	5
6	5001	5

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
0.0b	(* a (pow k m))
0.0b	(+ (+ 1.0 (* 10.0 k)) (* k k))
2.1b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
16×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
7×	`associate-r`
6×	`fma-def` `prod-exp`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `div-exp` `sum-log` `log1p-expm1-u`
3×	`flip3-+` `times-frac` `associate-l` `associate-/r*` `flip-+` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-exp` `associate-/r/` `cbrt-unprod` `sqr-pow`
1×	`associate-+l+` `frac-2neg` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 88

Calls

4 calls:

6.0ms	(+ 1.0 (* 10.0 k))
11.0ms	(* a (pow k m))
24.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
36.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+ 1.0 (* 10.0 k))
58.0ms	(* a (pow k m))
18.0ms	(+ (+ 1.0 (* 10.0 k)) (* k k))
124.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify57.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	477	629
1	2275	544
2	5001	524

prune458.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (fma 10.0 k (* k k)))
0.0b	(* a (pow k m))
0.0b	(fma 10.0 k (* k k))
2.1b	(/ (* a (pow k m)) (+ 1.0 (fma 10.0 k (* k k))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-exp-log`
16×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
11×	`add-cbrt-cube`
10×	`add-cube-cbrt`
7×	`associate-r`
6×	`prod-exp` `add-log-exp`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `times-frac` `div-exp` `associate-/r*` `log1p-expm1-u`
3×	`fma-def` `associate-l` `distribute-lft-out` `unswap-sqr`
2×	`cbrt-undiv` `pow-to-exp` `flip3-+` `pow-exp` `associate-/r/` `cbrt-unprod` `flip-+` `fma-udef` `sqr-pow`
1×	`+-commutative` `associate-+r+` `frac-2neg` `clear-num` `sum-log` `-commutative` `div-inv` `associate-/l`

Counts

4 → 84

Calls

4 calls:

6.0ms	(+ 1.0 (fma 10.0 k (* k k)))
11.0ms	(* a (pow k m))
0.0ms	(fma 10.0 k (* k k))
17.0ms	(/ (* a (pow k m)) (+ 1.0 (fma 10.0 k (* k k))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ 1.0 (fma 10.0 k (* k k)))
60.0ms	(* a (pow k m))
54.0ms	(fma 10.0 k (* k k))
120.0ms	(/ (* a (pow k m)) (+ 1.0 (fma 10.0 k (* k k))))

simplify51.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	395	565
1	1854	493
2	5002	486

prune254.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma k k (fma k 10.0 1.0))
0.0b	(fma k 10.0 1.0)
0.1b	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
3.8b	(/ (fma k k (fma k 10.0 1.0)) a)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

172×	`times-frac`
96×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
42×	`unpow-prod-down`
19×	`add-exp-log`
16×	`associate-/r*`
14×	`sqr-pow`
11×	`add-cbrt-cube`
10×	`div-exp` `div-inv` `associate-/l*`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `fma-udef`
1×	`associate-/r/`

Counts

4 → 181

Calls

4 calls:

0.0ms	(fma k k (fma k 10.0 1.0))
0.0ms	(fma k 10.0 1.0)
14.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
5.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

series222.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(fma k k (fma k 10.0 1.0))
38.0ms	(fma k 10.0 1.0)
115.0ms	(/ (pow k m) (/ (fma k k (fma k 10.0 1.0)) a))
46.0ms	(/ (fma k k (fma k 10.0 1.0)) a)

simplify86.0ms

Algorithm

egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	715	1922
1	3280	1854
2	5002	1852

prune538.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 10.0 k (* k k))
0.0b	(/ (/ (* a (pow k m)) (sqrt (+ 1.0 (fma 10.0 k (* k k))))) (sqrt (+ 1.0 (fma 10.0 k (* k k)))))
12.4b	(sqrt (+ 1.0 (fma 10.0 k (* k k))))
12.4b	(sqrt (+ 1.0 (fma 10.0 k (* k k))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac`
106×	`*-un-lft-identity`
96×	`sqrt-prod`
64×	`add-sqr-sqrt`
58×	`add-cube-cbrt`
24×	`distribute-lft-out`
22×	`sqrt-div`
20×	`add-exp-log`
18×	`associate-/r/`
13×	`add-cbrt-cube` `associate-/l*`
11×	`flip3-+` `flip-+`
9×	`div-exp` `div-inv`
7×	`associate-/r*`
6×	`pow1`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `cbrt-unprod` `fma-udef` `associate-/l/`

Counts

4 → 182

Calls

4 calls:

0.0ms	(fma 10.0 k (* k k))
34.0ms	(/ (/ (* a (pow k m)) (sqrt (+ 1.0 (fma 10.0 k (* k k))))) (sqrt (+ 1.0 (fma 10.0 k (* k k)))))
7.0ms	(sqrt (+ 1.0 (fma 10.0 k (* k k))))
7.0ms	(sqrt (+ 1.0 (fma 10.0 k (* k k))))

series271.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(fma 10.0 k (* k k))
120.0ms	(/ (/ (* a (pow k m)) (sqrt (+ 1.0 (fma 10.0 k (* k k))))) (sqrt (+ 1.0 (fma 10.0 k (* k k)))))
52.0ms	(sqrt (+ 1.0 (fma 10.0 k (* k k))))
48.0ms	(sqrt (+ 1.0 (fma 10.0 k (* k k))))

simplify87.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	689	3055
1	2932	2721
2	5001	2705

prune441.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes75.0ms

Accuracy

98.6% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.0b

bsearch43.0ms

Steps

Iters	Range		Point
6	2.2350332021713927e+140	1.354140707208992e+141	2.5838568036571295e+140

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	33
1	51	33
2	51	33

end0.0ms

sample1.1s

Algorithm

intervals

Results

476.0ms	12068×	body	80	valid
149.0ms	4430×	body	80	nan